Yes and no.
Some of life challenges come naturally. I don't believe God puts everything in our way, but he does use those things to help us learn and grow, if we choose to let him help us.
Some things come as a direct result of our poor choices. For instance, when we smoke, we get addicted. God didn't give us our addiction; it came as a direct result of our choosing to smoke.
Some trials come as a direct result of what other people do. We have our agency, and even when we choose correctly, others (who also have their agency) might choose poorly, and that can often be disastrous for us. Murder, rape, theft, etc; God didn't do that, people exercised their God-given agency and caused bad things to happen. Again, God can help mold these instances for our benefit and learning.
When we pray for strength, patience, charity, etc., these are the times I feel that God gives us those trials to test us, to help us learn from those trials and increase those Christlike attributes. Let's face it, if we pray for humility, God will humble us. I don't think it is in the program for us to magically gain whatever we pray for.
Even if we don't pray for it, God may "test" us by sending a little challenge now and again, but I think most trials are not sent by God, but used by God for our learning and experience.